Hodges' Model: Welcome to the QUAD: space

Hodges' model is a conceptual framework to support reflection and critical thinking. Situated, the model can help integrate all disciplines (academic and professional). Amid news items, are posts that illustrate the scope and application of the model. A bibliography and A4 template are provided in the sidebar. Welcome to the QUAD ...

Showing posts with label space. Show all posts
Showing posts with label space. Show all posts

Tuesday, October 13, 2026

Informação Relevante | [Docentes] 8.ª Edição dos Projetos Semente da UC | 8th Edition of UC Seed Projects – Applications open from 26 October to 27 November

Caros Investigadores,
Caras Investigadoras,

A Universidade de Coimbra vai lançar a 8.ª Edição do concurso Projetos Semente de Investigação Interdisciplinar, financiado pela Fundação Santander Portugal.

As candidaturas estarão abertas de 26 de outubro a 27 de novembro de 2026.

O concurso destina-se a investigadores/as em início de carreira, até dez anos após a conclusão do doutoramento, que pretendam desenvolver projetos de investigação interdisciplinares e alinhados com as Áreas Estratégicas da UC, promovendo a independência científica, a colaboração entre diferentes áreas do conhecimento e o desenvolvimento de competências de liderança.

Nesta edição serão atribuídos cinco prémios, um por cada Área Estratégica da UC, no valor de 20 000 € por projeto, correspondendo a um financiamento total de 100 000 €.

À semelhança das edições anteriores, o concurso pretende incentivar a colaboração entre investigadores/as de diferentes áreas científicas. Cada equipa deverá integrar investigadores/as de pelo menos duas unidades de investigação distintas da Universidade de Coimbra.

Convidamos os/as investigadores/as elegíveis a conhecerem esta oportunidade e a explorarem a possibilidade de desenvolver uma proposta interdisciplinar com colegas de outras áreas.

A página da 8.ª edição, incluindo o regulamento, o modelo de candidatura e as restantes informações, estará disponível a partir de 26 de outubro, data de abertura do concurso, em: Projetos Semente da UC

Com os melhores cumprimentos,

João Ramalho-Santos
Vice-Reitor para a Investigação
_____________

[EN]

Dear Researchers,

The University of Coimbra is launching the 8th Edition of the Seed Projects for Interdisciplinary Research, funded by Santander Portugal Foundation.

Applications will be open from 26 October to 27 November 2026.

The call is aimed at early-career researchers, within ten years of completing their PhD, who wish to develop interdisciplinary research projects aligned with UC’s Strategic Areas, fostering scientific independence, collaboration across different fields of knowledge, and research leadership.

This edition will support five projects, one in each of UC’s Strategic Areas, with €20,000 awarded to each winning project, for a total funding of €100,000.

As in previous editions, the call encourages collaboration between researchers from different scientific fields. Each team must include researchers from at least two different research units from distinct domains at the University of Coimbra.

We encourage eligible researchers to learn more about this opportunity and consider developing an interdisciplinary proposal together with colleagues from other areas.

The 8th Edition webpage, including the call rules, application template and further information, will be available from 26 October, when the call officially opens, at:

UC Seed Projects

Kind regards,

João Ramalho-Santos
Vice-Rector for Research
_______________________________________________
Universidade de Coimbra • www.uc.pt
Com os melhores cumprimentos,

Marta Santos
(Pelo Secretariado)

Thursday, September 10, 2026

Is the Individual-Group axis health's proscenium arch?

Speech: “All the world’s a stage”

By William Shakespeare
(from As You Like It, spoken by Jaques)
          
     All the world’s a stage, 
And all the men and women merely players; 
They have their exits and their entrances; 
And one man in his time plays many parts, 
His acts being seven ages. At first the infant,
Mewling and puking in the nurse’s arms; 
And then the whining school-boy, with his satchel
And shining morning face, creeping like snail
Unwillingly to school. And then the lover,
Sighing like furnace, with a woeful ballad 
Made to his mistress’ eyebrow. Then a soldier,
Full of strange oaths, and bearded like the pard,
Jealous in honour, sudden and quick in quarrel,
Seeking the bubble reputation
Even in the cannon’s mouth. And then the justice,
In fair round belly with good capon lin’d,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part. The sixth age shifts
Into the lean and slipper’d pantaloon,
With spectacles on nose and pouch on side;
His youthful hose, well sav’d, a world too wide
For his shrunk shank; and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound. Last scene of all,
That ends this strange eventful history,
Is second childishness and mere oblivion;
Sans teeth, sans eyes, sans taste, sans everything.

Source: https://www.poetryfoundation.org/poems/56966/speech-all-the-worlds-a-stage


TIME FRAMES

'As Shakespeare and his contemporaries wrote for the epic scale, the imaginative commitment and the 360-degree embrace of the Globe so, three hundred years later, generations of playwrights wrote for the velvety darkness, the enclosed acoustic and the picture framing of the proscenium arch.

For a century, the story of the changing world was told inside proscenium theatres, by a series of remarkable playwrights. In over sixty irreverent, illuminating pen portraits – of both famous giants and lesser-known talents – Dominic Dromgoole takes us on a journey from 1865 to 1965, revealing how these writers used the framed stage to reflect the social upheavals of their times.' 

This post began with: 'All the world's a stage', but I realised I'm no Shakespeare. Hodges' model is a frame; and users of the model can put it to work, readily. Be that in the sciences, arts, and across curricula. The 'arch' in Hodges' model appears to be inverted, working from within, rather than out. Similarly to the proscenium arch, however, the model provides a structure, for whatever performance, situated, will surely follow.

Hodges' model: Axes and Domains

Of course, the question posed here might be re-framed as: 

Are the axes of Hodges' model, life and death's proscenium arch?


Dominic Dromgoole (2026) Time Frames: A century of proscenium playwrights. London: Faber. 
https://www.faber.co.uk/product/9780571374113-time-frames/ [Text source].

Previously: 'drama' : 'stage' : 'frame'

Monday, August 03, 2026

The Sciences: Points, lines, angles and perspectives on Domains

In Hodges' model the axes are presented - by convention - as perpendicular. From this it follows that the resulting four domains, or quadrants appear as equivalent in terms of the space they each occupy. There are many posts on the blog that present a 2x2 table. When in template form Hodges' model is also a potential corpus, empty apart from its structure, then there must surely be a gross asymmetry in the SCIENCES domain compared with the others, including the SPIRITUAL. Discuss?

#simplicity #complexity #folktheory #humanities #arts #humanistic #emotion #balance

See also: https://hodges-model.blogspot.com/2026/06/h2cm-domains-symmetry.html

Monday, June 29, 2026

Where is the Centeredness of Care?

In trying to see Hodges' model anew, which is quite a challenge after four decades; what of the model's structure?

It is easy to get carried away with mathematical terminology:

One line, add another, and they intersect, at a 90 degree right angle. So is centeredness to be found at the intersection point? 

If I'm tying myself up in knots well there's another possibility! 😉 

As a whole it appears the axes of the model are a manifold and not - in the center?

What do you think?


See also: 'What Is a Manifold?'

https://www.quantamagazine.org/what-is-a-manifold-20251103/

Saturday, June 06, 2026

"step inside" TO "think outside"

  
individual
|
INTERPERSONAL
: SCIENCES             
humanistic ------------------------------- mechanistic
SOCIOLOGY : POLITICAL   
|
group



 










             c/o Somerset House, 6th June 2016.

Sunday, May 17, 2026

Wittgenstein's - Tractatus

Apparently, Wittgenstein walked away from philosophy after publication of the Tractatus. He thought he had solved the problems of philosophy, logic and reality.

In trying to ‘see’ Hodges’ model, in mathematical terms, there may be lessons in Wittegenstein’s approach, both in content and style. Of course, as a non-mathematician, I probably should leave well-alone; and stick to nursing. But that is the problem: from 1987-88 there is a need for a different perspective, even if this is a personal challenge. As with many ‘reviews’ here, we can look at Wittengenstein’s work, reflect upon it, and consider how it relates to the purposes, structures and content of Hodges’ model.

The Tractatus’s first line then, offers a warm welcome.

‘The world is everything that is the case.’ [I]

Making the decision to become a nurse and enrolling as a student makes you an educational and workforce demographic case.

Once a student in the university lecture theatre, you hopefully whether consciously, or not are exposed to the theory – practice gap; as you yearn to be on your first placement. Now it you who is seeking ‘cases’. As we live, and statistics roll and tally, the question of caseness (and categories) is key, one that is carried around even if not always active, recognised as such.

As noted in the previous post, we can for Hodges’ model (and other models, frameworks it must be said) think of ‘case’ as a, or the situation. 

A mathematical approach to Hodges’ model involves looking at things, concepts, people as objects. This includes patients and carers. In terms of a project worthy of pursuing in nursing and other disciplines involved in healthcare, this mathematization presents a non-trivial challenge. A fully-deserved response would be: 'What have you done to the aptitude for care and caring attitude? You've cancelled - subtracted it!' Humour aside:

'In order to know an object, I must know not its external but all its internal qualities.' [2.01231] 

Is this equivalent to us getting to know our patient / client and their socio-political context? 

‘The way in which objects hang together in the atomic fact is the structure of the atomic fact.’ [2.032] 

It is a help that Wittgenstein points to structure (crumbs of understanding are welcome here, as incremental steps). In formulating Hodges’ model we first identify the axes. It is the axes that then provide a space, four domains in total, to frame the objects that we decide; or, as the situation dictates, what concepts are placed in the domains of Hodges' model.

There is a successive series that follows, combining place, space and logic: ‘The proposition determines a place in logical space: the existence of this logical place is guaranteed by the existence of the constituent parts alone, by the existence of the significant proposition.’ [3.4]

‘The propositional sign and the logical coordinates : that is the logical place.’ [3.41]

‘The geometrical and the logical place agree in that each is the possibility of an existence.’ [3.411]

‘Although a proposition may only determine one place in logical space, the whole logical space must already be given by it.
(Otherwise denial, the logical sum, the logical product. etc., would always introduce new elements -in co-ordination.) 
(The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)' [3.42]

While Wittgenstein came to view ‘the picture theory of meaning’ as incorrect, as a conceptual framework and diagrammatic resource Hodges’ model is closely tied to this form of representation.

Of course, the logic at work here, is far from mathematical, but there is surely a logic.

'Formal concepts cannot, like proper concepts, be presented by a function.' [4.126]

'There is therefore really a sense in which in philosophy we can talk of a non-psychological I.
The I occurs in philosophy through the fact that the "world is my world'".
The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit - not a part of the world.' [5.641] 

'Although the spots in our picture are geometrical figures, geometry can obviously say nothing about their actual form and position. But the network is purely geometrical, and all its properties can be given a priori.

Laws, like the law of causation, etc., treat of the network and not of what the network describes.' [6.35]

There is much more in this work, and much that remains a challenge. Many commentators have written and said in interviews that the Tractatus rewards re-reading and some sentences stay with you for life (The Great Philosophers BBC TV). 

I'm still seeking mine.

https://www.gutenberg.org/files/5740/5740-pdf.pdf

Friday, April 17, 2026

Ann Hutchinson Guest (Obit.), 'Authority on dance notation ... '

'Although there are many forms of dance notation going back to Pierre Beauchamp's system for Baroque dance in the 1680s, Nijinsky had developed his own cryptic version. Ann Hutchinson Guest first tried to reconstruct his work in 1956 after the choreogapher's widow, Romola, gave her his notes. "I spent years trying to work it out," she said, adding with a laugh: And I'm supposed to be the leading authority on dance notation in the world. She told how Nijinsky had revised his notes many times, often contradicting himself. 'We couldn't get anywhere. Romolo was furious. She said it was taking much too long."
    Hutchinson Guest studied dozens of different dance notation systems, translating many of them into Labanotation, a system developed in the 1920s by Rudolf von Laban who was a central figure in European modern dance. According to a  press report in 1954: "The printed Labanotation page looks like a combination of hieroglyphs, pictographs, Morse dots-and-dashes, đoodles, and a musie score turned on edge" 
    It was not until 1980 that she and Claudia Jeschke, a dance historian, succeeded in cracking Nijinsky's code after finding a copy of his annotated score in the British Library.'
Register, The Times.

My source: Ann Hutchinson Guest (Obit.), 'Authority on dance notation known for reconstructing Vaslav Nijinsky's scandalous ballet, L'Après-midi d'un faune'. Register, The Times. 20 April, 2022, p.48.
https://www.thetimes.com/uk/obituaries/article/ann-hutchinson-guest-obituary-hkw8z88ns


INDIVIDUAL
|
     INTERPERSONAL    :     SCIENCES               
HUMANISTIC --------------------------------------  MECHANISTIC      
SOCIOLOGY  :   POLITICAL 
|
GROUP
abstraction
representation
interpretation
observation - translation
code - formalism

body (bodies)
symbols - forms
dance
choreography
movement - 4D - time

group
ensemble
'anthropological composition?'
'diagnostic grouping'?
social - cultural category . . .

'collective power & attention 
evinced as time'
'The stage: the space for health'^

Hutchinson Guest in 1956
 Source: The Times.


'Dance has been called moving architecture, a truth which the complexities of contemporary choreography may mask. Not only does the dancer's body form shapes and groups of dancers form moving or static designs, but also group arrangements carve up the stage space, establishing areas of open as well as enclosed space which are significant in their changes and contrasting effects.

While the rccording of movement on paper-dance notation-does not look like movement (disregarding primitive stick figure drawings), there is an "architecture" in the sequence of graphic symbols used to record dance patterns. Over the centuries many different devices have been used to capture dance steps on paper. What are the elements that have to be represented?

The process of dance notation requires reducing four-dimensional movement (time being the fourth dimension) to a two-dimensional surface. The parts of the body in action have to be defined, as does the form of movement involved (flexion, extension, rotation, directional placement) and the duration of each in relation to the overall time structure. In group dances the relationship of dancers to one another must be determined and recorded, as well as their location on stage and their paths of travel. In a dance score each performer is like a small orchestra-arms, legs, head, torso, etc. in motion-this is then multiplied by the number of dancers who are performing individual sequences.'


Guest, A. H. (1990). Dance Notation. Perspecta, 26, 203–214. https://doi.org/10.2307/1567163

^Health is always performed in the political domain, make no mistake (excuses, or exceptions). It is not:
  1. Acknowledged, masked - covered by the 'set design' (see #2 below);
  2. Implied in the medical, biomedical, bio-psycho-social model;
  3. The intermission is neither the time, or place, to reflect upon and critique the political in health :: health in politics.

Previously: 'dance' : 'architecture' : 'movement' 
 : 'notation'

Saturday, April 04, 2026

Apollo - Artemis II and the Joy of Earth

Since Artemis II was launched, several more-senior people in the media have been interviewed, with their reflections on certain lunar events in 1969 with the Apollo programme.
 
I too remember being woken up, taking several giant steps down the stairs and huddling around the black & white TV set in the early hours. I'm so glad I did that.
 
Thanks mum and dad. X
 
Following the livestream from Artemis, it's brilliant to see Christina Koch and Victor Glover onboard too.
 
INDIVIDUAL
|
    INTERPERSONAL    :     SCIENCES               
HUMANISTIC --------------------------------------  MECHANISTIC      
SOCIOLOGY  :   POLITICAL 
|
GROUP
 

art002e008487 (April 4, 2026) - NASA astronaut and Artemis II mission specialist Christina Koch peers out of one of the Orion spacecraft's main cabin windows, looking back at Earth, as the crew travels towards the Moon.


"I have not complained about the weather one single time. I'm glad there is weather. I've not complained about traffic. I'm glad there are people around. One of the things that I did when I got home - I went down to shopping centers, and I'd just go around there, get an ice cream cone or something, just watch the people go by, and think: "Boy, we're lucky to be here. Why do people complain about the Earth? We are living in the garden of Eden."

                    Alan Bean. Apollo 12



 




Sunday, March 15, 2026

viii Book: Bill Ross - 'Order and the Virtual'

 'The Philosophy and Science of Deleuzian Cosmology'

So much of what we experience is nuanced. What was conscious thought, becomes tacit knowledge and unconscious. Is that consciousness nullified as Ross writes on page 76? I wrote a note 'reflection as hesitation'; also prompted to think about intution (p.83) and our word uses in 'retardation' (which here is no problem at all - in physics and complex sciences/systems. Again the 'principle of least action' arises (p.82). With more physics and cosmology to follow, it helps a little that 'manifold' has landed begging to be understood across the contexts. Bill Ross notes how Delueze and Michel Serres used the game metaphor [Game analogy #1]. Again, lifting this to a scribble 'Health-Illness is quite a game'! This will be the subject of a post soon. In England at least the law and manifold on health (being productive) and illness has been utterly disrupted. The game-table has been kicked over, by those in society who still able? New spaces, and canvases are needed. Kantian thought and interpretations are added to Leibniz. A heady mix but clearly essential as Bill Ross's critique is developed. 
 
The book was a must-read, as in the contents: Complexity (with a presentation next month), cosmology, Serres, and Claude Shannon. In Game Analogy #2, "Communication is understood here to encompass much more than meaningful exchange; all phenomena 'communicate'". p.85. I couldn't agree more with with these 'games', this thought being 'situated within the purchase of information theory' (p.86). Bizarrely (or not), in the same year two papers:
Jones, P. (1996) Humans, Information, and Science, Journal of Advanced Nursing, 24(3),591-598.

Jones, P. (1996) An overarching theory of health communication? Health Informatics Journal,2,1,28-34. 
Ross explains the global view of Michel Serres when it comes to 'information'. This entranced me, and I only scratched the skin:
Jones, P. (2008) Exploring Serres’ Atlas, Hodges’ Knowledge Domains and the Fusion of Informatics and Cultural Horizons, IN Kidd, T., Chen, I. (Eds.) Social Information Technology Connecting Society and Cultural Issues, Idea Group Publishing, Inc. Chap. 7, pp. 96-109.
Here there's a pointer to the cosmology to follow - Ross is true to the title. I have let most of the Astronomy Yearbooks go, but retain a few. Not just for key birth-years, but articles that are well written and researched historical snapshots. Here, Bill Ross discusses the game of Cepheid variables and their significance in mapping the universe. Truly, fascinating. Weaver's three levels of salient action are listed. Threads are tied too, with conclusions offered. These rules are reappraised, physics ever present. In light of one of the above papers I should revisit Serres, and Leibniz; the search for 'overarching explanatory power' (p.91) is ongoing. This game draws on Serres invitation to imagine a diagram, a network of nodes, channels, and propositions. This tabular formulation and its relations for me, spans the history of economics (Quesnay's tableau), the current state of economics (human values), and next (mathematical?) steps for Hodges' model. So many questions here: surely node  can't be an axis? I felt like Hansel, picking up sweets, Cartesian lines, scalene forms, thresholds, coming across hoops to jump through through to terminal equilibri. As you walk the sound of the thalweg, downstream... where Bergson features once again.
 
Reading Ross, over several months coincided with several key themes gaining in personal coherence. Bayesian ideas as might be applied to Hodges' model, even if in a naïve way (c/o feedback on draft notes). The remainder of chapter 3 includes time (thought), percept (space), to close with Deleuze's Ideal Game. I looked up Cortázarian Hopscotch https://en.wikipedia.org/wiki/Hopscotch_(Cort%C3%A1zar_novel), as the preface is titled. Ross reflects on the Ideal Game (does it exist, for Deleuze, only in thought?), and the distinction between 'domestic' chance (Baysian) and radical contingency belonging to the clinamen. In response to 'physical action and and the thought being on the same continuum', don't ask (please!), but I scribbled: 'corridor care' - a dangerous game, far from ideal. Plus, bird's using quantum entanglement to navigate. 'Kant's chaotic manifold', I will also investigate for next month(?).
Chapter 4 'Order as Complexity' proved most relevant. Every page is touched by graphite.

Deleuze has a 'blind spot' (p.111), something that Hodges' model seeks to ameloirate. But then of course at the model's center (nexus - as noted) that decussation of the axes invites a darkness of its own. If Hodges' model assists forethought and foresight  While inviting complexity, this interdisciplinary palette can also facilitate trandiscipinary sense-making. 'Magnitudes of intensity' reminded me of logarithmic thresholds within our perceptual apparatus. This is like reading Serres. A flow of punctum, simultaneity, delay (again) but its contribution to causal series, and Aionic time. I was taken (frequently)  to plane, person, personhood, chronicity, scales, local to global to glocal.

There is a 'corner' amid those thousand plateaus. n.b. to self - 'triangulation always needs one other'. I cannot resolve the frameworks as yet, scientific - otherwise or otherwhere; but you can take flight from here. Physics takes it place as 'complexity begets complexity'. Bill Ross utilises well-recognized sources, Penrose, Kauffman, Kolmogorov and Bohm.

As with the frameworks internal and external complexity must be untangled 1-4 (p.124?). I can laugh now, did I really try to marry up Order  - Disorder :: Simple - Complex (complicated?) to the domains of Hodges' model? So often reading philosophy, you feel an imposter playing games with words, as in: 'different similarities' and 'similar differences' (p.125). But of course, this is serious scholarship. Especially, when it involves lines, a rough circle, segments and dimensions: disorder becomes different degrees of order. Page 126 delivers Deleuze in spades, Ross pulls his thoughts together. It is fitting for me that Ross closes chapter 4 with a nod to transdisciplinarity.
Chapter 5 deals with symmetry and disymmetry; indifference and difference; limits and non-locality. There is an argument to follow (p.133). With 'group theory' mentioned on p.131, I've a lot of things to 'look up' [topology too]. Despite appearances I recognise the lack of symmetry in Hodges' model. This is what the situation does (practice) and means (theory): 'There is no reason under the sun which can rely on perfect symmetry' (p.135).  Where do/can we locate 'spooky action at a distance' in Hodges' model (p.140)? 

The Higgs role! Who knew? 'the speed of light. It represents a retardation.' Thanks Bill Ross, fascinating pp. 135-174. Plus, axes too. Note to self: when we die do we 'simply' set sail on the Dirac Sea? Attending the Bill Ross Memorial Workshop – BSP Special Event 2025 last September:

https://hodges-model.blogspot.com/2025/09/bill-ross-memorial-workshop.html

the esteem .. and love .. that Bill Ross engendered in the people that knew him. The preface refers to chats in university cafes. How I wish. I wonder what Bill would have made of Hodges' model and the ongoing project here? Vitally, I get a distinct sense that he would have found time to listen ... 
'Bill Ross (1964 – 2022) had interests ranging widely across contemporary philosophy and culture, with a particular interest in the relations between science and philosophy. As managing editor, he was the driving force behind Clinamen Press, which in the early 2000s published new works by contemporary philosophers, and English translation of important works by continental philosophers such as Henri Bergson, Gaston Bachelard and Michel Serres. He completed his PhD in philosophy at Staffordshire University, where he taught on the MA in the Philosophy of Nature, Information, and Technology. Bill had a lifelong passion for the connections between science and philosophy, on which he had published several important articles. Bill was working on a monograph on the philosophy and science of Deleuzian cosmology, which was has been posthumously published by Edinburgh University Press. This event is to celebrate Bill’s book and his life, and to allow his friends, his colleagues, and anyone interested in his work or the topics and issues addressed by his work to continue the conversation that Bill’s work inspires.'
https://www.thebsp.org.uk/bill-ross-memorial-workshop-deleuzian-cosmologies/
 
Many thanks again to Edinburgh University Press for my copy - a keeper! Bill Ross RIP.
 
Bill Ross (2024) Order and the Virtual: The Philosophy and Science of Deleuzian Cosmology. Edinburgh: Edinburgh University Press.
https://edinburghuniversitypress.com/book-order-and-the-virtual.html

Sunday, February 15, 2026

vii Book: Bill Ross - 'Order and the Virtual'

'The Philosophy and Science of Deleuzian Cosmology'

On the publisher's site, the content listing is limited to the chapter (section) titles (as shared in iii). 

There is also one review:

'In classical physics and its mechanical paradigm, events are stories about fundamental objects. In quantum physics, it is the objects that are the stories by which we understand physical systems in their most fundamental form--as histories of events. In Order and the Virtual, Bill Ross makes a compelling case that the event-ontological philosophies of Deleuze and Whitehead will become for the new physics what the philosophies of Newton and Locke were for the old.'

– Michael Epperson, Research Professor and Director, California State University, Sacramento
[ https://edinburghuniversitypress.com/book-order-and-the-virtual.html ] 

It is worth listing the content details in full:

Series Editor's Preface vii
Preface by Robin Durie and David Webb ix
Abbreviations xii

Chaos I
Chaos and Complexity Theory I
Nietzschean Chaos and the Superior Principle of Sufficient Reason 5
The Eternal Return and the Disparity of Forces 8
Ergodicity and Infinite Duration 10
Post-Classical Physics and the Question of Entropy 15

2. Entropy and the Complete Concept in Leibniz and Deleuze 24
Dissymmetry, Energy Gradients and the Ultimate Origination of Things 29
On the Ultimate Origination of Things 30
From Many Worlds to Chaosmos 34
The Calculating God 36
Mathematical Thought, the Problem and the Cosmos 38
The Compete Concept and Disjunctive Synthesis in Sufficient Reason 44
Physical Systems, Disparity and Disjunctive Synthesis 50
Chaosmos as Cosmology 56
Absolute Zero, Limits and the Infinite 60
Simple Order 68

3. Order 71
Mechanism and Vitalism, Order and Complexity 73
The Game Analogy #I: Leibniz and Kant 81
The Game Analogy #2: Claude Shannon and Michel Serres 83
Game #2.1: Claudo Shannon's 'A Mathematical Theory of Communication' 86
Game #2.2: Michel Serres The Birth of Physics 94
Game #3.0: Deleuze's Ideal Game 98

4. Order as Complexity 109
Complexity as Principle 122
Limits without Negation 127

5. Sufficient Reason as Dissymmetry and the Evolutionary Paradigm 131
Limits and Non-Locality 135
A Network Paradigm: Loop Quantum Gravity 150
A Holographic Paradigm: David Bohm's Implicate Order I54
Evolutionary Expansiveness 161

Conclusion 175
Notes 182
Bibliography 207
Index 217

I can see why my reading of OatV is not at the usual 21st century pace. 'Section 2. Entropy and the Complete Concept in Leibniz and Deleuze', pp.24-68, as already noted, is a real melange of ideas from several sources. As noted already, you have to unpick Deleuze, Simondon and Ross's guiding thought. your reading and purpose also matters however; an amazing gift of texts like this.

'CHAOSMOS AS COSMOLOGY

If energy gradients are the sufficient reason of all that appears for ther- modynamics, symmetry is to most intents and purposes the sufficient reason from which modern physics draws its rationale. Mathematical relations of symmetry have come to take the place of 'law` in classical physics: where there is symmetry, science identifies an underlying order, As we shall see, however the point of contention between Deleuze and the prevailing scientific consensus is by no means so black and white. and far from universally upheld among the scientific community. Once again, it is in the particularities of this tension that productive exchange may be found.' p.56.

Leibniz's 'individual' (and monads) differs from that in Hodges' model, but there is the question of time and scale (at both ends of the vertical axis in Hodges' model):
'Each individual is in contact with, expresses, all individuals in the world, but obscurely, again, as with Leibniz, through infinitely ramifying lines of divergence.' p.54.

'Each individual, then, remains necessarily the sum of all its predicates, but in the same sense as a singularity contains its own power of expressing innumerable contradictions; here is Deleuze's 'object = x', the concept which overcomes the idea of world understood merely as a circle of convergence.' p.55.

We often speak in terms of 'take-aways'. Ross provides a packed (yet nutritious!)  lunch and really useful snippets:

'Disjunction becomes a relation' (p.49).

Identity runs through section 2. Difficulties of orientation are noted. I wondered about a symbol for singularity, but I cannot find one(?). Ross, himself, describes as dense, Leibniz's essay on 'Origination'.

Is the nursing process, predicated up Aristotlean 'hylomorphism' (p.50)? To capture the (cognitive) orientation of an individual, do we locate the basis for the immanence of nursing, in problems that are potential, or actual?

Amongst, particle physics, absolute zero, a two-dimensional plane, and 'symmetry'; I found 'ill health'. At least, I did in a spontaneous pencilled note. And, nearby: 'Symmetry is Law'; (p.59)'.

There is grist-for-the-mill in producing new formulations for Hodges' model. Do 'non-commutative relationships, and vectorial transformations abound? (p.60)

Health and ill-health break symmetry (which Deleuze resists), and do so within and across all the domains of Hodges' model.

Ross quotes in Section 3 'Order', page 73 in Bergson's Creative Evolution (236): '[The mechanistic order] may be defined as geometry which is its extreme limit; more generally, it is that kind of order that is concerned, whenever a relation of necessary determination is found between causes and effects'. I could go on ... but scribbled 'cogeography/cogeographical'.

Many thanks to Edinburgh University Press for my review copy.

More to follow here ...

Bill Ross (2024) Order and the Virtual: The Philosophy and Science of Deleuzian Cosmology. Edinburgh: Edinburgh University Press.
https://edinburghuniversitypress.com/book-order-and-the-virtual.html

Wednesday, January 28, 2026

ii Math Without Numbers - final notes & obs

In Math Without Numbers the chapters and topics flow and slot in really well, even for novices. There is no index, the inclusion of which is a first-check usually. The book's appeal was its non-technical title and invitation reading the sleeve notes. The title throws up words and visuals, the latter, to repeat, are ably and simply furnished by M Erazo. Remaining notes to highlight (record here) include (and capture overthinking!):

Math Without Numbers

Reference to 'ideology space', 'conceptual space' and the role of visual analogies, idioms, and how 'the list of spaces to choose from is always the same.' ... pp.28 & 29. On page 30, 'When you say that gender is a spectrum rather than a binary, that's a topological claim: You're  saying gender space is one-dimensional (a line) rather than zero-dimensional (two separate points). 'Questions about which conceptual paradigm to use sometimes boil down to questions of dimensionality.' Discussion of an infinite continuum had me making an axis of Hodges' model warp, this way and that: concave-convex (p.59). Maps and correspondence is already well established, as per a new paper (abstract and thanks to follow 1st Feb):

S. Bettiol, P. Jones, H. A. Onyedikachi, and W. G. Kernohan, “Bridging Gaps in Oral Health Frameworks: Mapping With Hodges' Health Career - Care Domains - Model”, Journal of Public Health Dentistry (2026): 1–14, https://doi.org/10.1111/jphd.70034 

Interesting to read of general map facts, flowing substances inside a rigid container, and vector maps. A pencilled note to share:

'Because when you look at things in the abstract like this, dusting off the specifics of a situation to focus on underlying dynamics, you start to realize there are only so many different patterns and structures out there. These patterns and structures are called mathematical objects, and thinking about them is called math.' p.79

The chapter on (generalised) Algebra, forced me to reconsider the Socratic, guided discovery and arrival at the structure of Hodges' model. (lines & points : nodes & edges). For page 88, I noted 'generic' invites abstraction. Isomorphism is discussed. Again I tested this against Hodges' model. I've always found it helps to immerse oneself in a new vocabulary: so welcome (anew) - structures, fields, rings, groups, loops, graphs, lattices, orderings, semigroups, groupoids, monoids, magmas, modules . . . algebras, p.101. Some are named only, but on graphs raises questions ... p.103.

'How densely interconnected is it? How segregated into different cliques? Does it cut clean into two subgraphs, with no connections between them? Can it be drawn without any lines crossing? Are there any lone dots without any connections?' 

There's the matter of 'friend of a friend' who have broken out of the sociological domain. Other notes to self: Significance of concepts - patient-centred, service-centred? The distance between between (vertical, horizontal, diametric)? There are weighted graphs (p. 104) and acknowledgement of category theory (p.115). A chapter on modelling pp.161-175, and models p.164 & p.169 are just a selection of highlights on a marvellous tour.

A hidden puzzle in the book remains a mystery for me.

Milo Beckman (2021) Math Without Numbers. London, Penguin Books. Illustrated by M. Erazo.

Previously: 'math' : 'diagrams' 
Plus, now archived Science domain links: 
https://web.archive.org/web/20150414125339/http://www.p-jones.demon.co.uk/linksTwo.htm

Believe it or not, this 'diversion' does help my reading of Order and the Virtual. 

Sunday, January 25, 2026

'Maths Without Numbers' by Milo Beckman

'Before you go tell your loved ones that you read a book about math and learned that a square is a circle, keep in mind: Context matters. A square is a circle, in topology. A square is most certainly not a circle in art or architecture, or in everyday conversation, or even in geometry, and if you try to ride a bike with square tires you won't get far.' pp.7-8.

'Like a line:

(Illustration - pen drawing of a line, a 'C' and an almost closed circle.)

A line can be bent almost into a circle, but to finish the job we'd need to click the ends together--not allowed. No matter how you manipulate a line, you'll always have those two special points on either end, where the shape just stops. You can't get rid of end-points. You can move them around and stretch them apart, but the two end-points are an unchanging feature of the shape.

For a similar reason, a figure-eight is a different shape too. There aren't any end-points, but there's still a special point in the middle where the lines cross, where there are four arms reaching out instead of the usual two at any other point. Stretch and squeeze all you want, you can't get rid of a crossing-point either. p.9.

Math Without Numbers
'The circle (aka S-one) and the infinite line (named R-one) are the only manifolds in the first dimension. To avoid end-points, you either have to loop back around or just go on and on forever. And don't forget: Because all the shapes in topology are stretchy, this also covers any closed-loop shape and any goes-on-forever shape. It doesn't have to be literally a circle or a straight line.' p.16.

The third dimension, dough-type manifolds, is pretty well understood at this point, though it took a hundred years and a million-dollar prize to get there, and we still don't have a totally neat and clean classification like the lower dimension. In dimensions five and up, topologists use a set of techniques called "surgery theory" to operate on manifolds and construct new ones.

That just leaves dimension four.

I wish I could tell you what's going on in dimension four. I'm not sure there's anyone who really knows. It's a weird boundary case: too many dimensions to do visually, but not enough to use sophisticated surgery tools. There are entire textbooks dedicated to what little we know about four-manifolds, and I couldn't make sense of anything past the opening pages. A professional topologist once told me she'd wanted to work on four-manifolds as an undergraduate but was advised to steer clear.' pp.23-24.

"Like a line" ... Yes. Take two that cross. Then the universes open up. 

Milo Beckman (2021) Math Without Numbers. London, Penguin Books. Illustrated by M. Erazo.

Previously: 'surgery'

Sunday, December 21, 2025

Disciplinary bridges ... how's your sense of direction?

As an advocate for Hodges' model, I've acquired an affinity for inter- multi- transdisciplinary bridges, especially medical sociology, those leading towards the mathematical, and human geography. An old but significant influence is:

Chapman, K. (1979). People, pattern, and process: an introduction to human geography. London: Edward Arnold.

Chapman begins with the concept of distance, speed of movement and the consequence of the shrinking world. Our ability to move faster has radically altered the total travel time: from what was a 50 mile walking-day. In chapter 2, 'A Conceptual Framework' refers to:

  • Decision making - the basic mechanism
    • The Spatial Context
    • The Content of Space
  • Dimensions of Space
  • Spatial Process - Causality in Time and Space

Overall, the book also takes me back to a paper I cited in 2007: Bell jars and bell curves

I'm sure the 'School of Geography' at Leeds is unrecognisable today from that of the 1980s. But the referenced paper in the 'Bell jars..' post:

Macgill, S.M. (1984). Structural Analysis of Social Data, A Guide to Ho's Galois Lattice Approach and A Partial Re-Specification of QAnalysis, Working Paper 416, School of Geography, University of Leeds. Abstract 1985

- still gives me an itch I can't scratch. 

 I could not fully understand, or follow, the print quality doesn't help, but it captured my imagination (perhaps that is enough?).

Chapter 9 stands out with 'Spatial Pattern' pp.203-234, 9.1.1 Topologic Structures, pp.205-209. Here, Chapman explains and has examples of connectivity matrices, with three indices to calculate the connectivity in a graph. All grist for the mill.

Happy Solstice too!

Thursday, December 11, 2025

Bourdieu: systems, axes, maps, practical logics

I have checked these quotes and am fairly sure they are accurate. The first, I feel, improves with re-reading, and presents a clearing at the end? 

The clearing could be a template, and as per the second it may be old; but retains its practical function.

'Intellectualism is inscribed in the fact of introducing into the object the intellectual relation to the object, of substituting the observer's relation to practice for the practical relation to practice. Anthropologists would be able to escape from all their metaphysical questioning about the ontological status or even the 'site' of culture only if they were to objectify their relation to the object, that of the outsider who has to procure a substitute for practical mastery in the form of an objectified model. Genealogies and other models are to the social orientation which makes possible the relation of immediate immanence to the familiar world, as a map, an abstract mode of all possible routes, is to the practical sense of space, a "system of axes linked unalterably to our bodies, which we carry about with us wherever we go", as Poincaré put it.' p.34.
The Logic of Practice
'The logical [kinship] relations he constructs are to 'practical' relations - practical because continuously practised, kept up and cultivated - as the geometrical space of a map, a representation of all possible routes for all possible subjects, is to the network of pathways that are really maintained and used, 'beaten tracks' that are really practicable for a particular agent. The family tree, a spatial diagram that can be taken in at a glance, uno intuitu and scanned indifferently in any direction from any point, causes the complete network of kinship relations over several generations to exist in the mode of temporal existence which is that of theoretical objects, that is, tota simul, as a totality in simultaneity. It puts on the same footing official relationships, which, for lack of regular maintenance, tend to become what they are for the genealogist, that is, theoretical relationships, like abandoned roads on an old map; and practical relationships which really function because they fulfil practical functions.' p.35.


My source:
Bourdieu, P. (1990). The Logic of Practice. Stanford University Press. https://doi.org/10.1515/9781503621749 [and image source].

Bourdieu, Pierre, "The Logic of Practice (1990)" (1990). eTextbooks for Students. 875.
https://stars.library.ucf.edu/etextbooks/875

See also: https://hodges-model.blogspot.com/search?q=bourdieu

Friday, November 07, 2025

Half-turns ... to orbit

individual
|
INTERPERSONAL : SCIENCES
humanistic -------------------------------------------  mechanistic
SOCIOLOGY : POLITICAL
|
group-population


 "If you can get your ship into orbit, you're halfway to anywhere."







See: Where did Heinlein say "Once you get to Earth orbit, you're halfway to anywhere in the Solar System"?

Thursday, October 30, 2025

In Browder, 'care' is mentioned over 150 times!

OK - so now you're teasing ...

'Surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory, without losing sight of the geometric motivation.' Ranicki, 2001. 
'IV. Surgery and the Fundamental Theorem

In this chapter we develop the techniques of surgery for constructing normal cobordisms and use them to prove the Fundamental Theorem. The ideas of surgery have their origins in the theory of 2-manifolds, in the process of "cutting off handles", and in general, in the theory of Marston Morse of non-degenerate critical points of differentiable functions.' Browder, 1972.

In Browder, care is mentioned over 150 times!

'Poincaré' that is.

individual
|
INTERPERSONAL : SCIENCES
humanistic -------------------------------------------  mechanistic
SOCIOLOGY : POLITICAL
|
group-population



'The Classifying Spaces for Surgery
and Cobordism of Manifolds'

Try to - follow the language* ...

"Follow the money!"


Ranicki, A. (2001) An introduction to algebraic surgery. Surveys on Surgery Theory, Volume 2, edited by Sylvain Cappell, Andrew Ranicki and Jonathan Rosenberg, Princeton: Princeton University Press, 2001, pp. 81-164. https://doi.org/10.1515/9781400865215-005

Browder, W. (1972) Surgery and the Fundamental Theorem. In: Surgery on Simply-Connected Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 65. Springer, Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-50020-6_4

Madsen, I. H., and Milgram, R.J., (1979) The Classifying Spaces for Surgery and Cobordism of Manifolds. Princeton University Press.

Image: https://m.media-amazon.com/images/I/41THEeVvpdL.jpg

*concepts!

Wednesday, October 29, 2025

Normansfield Theatre in Teddington

Normansfield Theatre in Teddington

'My favourite building is the amazing Normansfield Theatre in Teddington that John Langdon Down (1828-1896) built to provide positive and stimulating education for learning disabled people (Down syndrome is named after him). At a time when most disabled people would have been shut away in horrific asylums, Down adapted his own house as a residential home, and built a beautiful theatre for creative rehabilitation. It's one of the few surviving private theatres from the period, with original painted scenery and other ornate fixtures, recently remodelled. For me, it's also a reminder of how the wealthy often used their money for good causes, which feels less common now. Jos Boys, guest curator and co-director of The DisOrdinary Architecture Project'


My source: The pick of London Open House. House&Home, FTWeekend. 6/7 September 2025. p.8.

Image: Langdon Down Centre

Previously: 'learning disability' : 'theatre' : 'architecture'

Monday, October 27, 2025

Health, planet, self: after - 'Can molecular Lego save the planet?'

Ack: © Johan Jarnestad /
The Royal Swedish Academy of Sciences

'This morning’s Nobel Prize in Chemistry is one that’s been anticipated for several years now: it goes to Susumu Kitagawa of Kyoto, Richard Robson of Melbourne, and Omar Yaghi of Berkeley for metal-organic frameworks.'
'So what’s a MOF? This goes back to the idea of “coordination chemistry”, a huge topic in the inorganic and metal-organic fields.'

 


The 2025 Nobel Prize in Chemistry: Metal-Organic Frameworks 


Can conceptual Lego - 'human-metal organic frameworks' -
save healthcare, planetary and self-care?

'One astonishing characteristic is the amount of surface area locked away in these new materials: a MOF weighing one gramme can have an internal surface area the size of a football pitch^. MOFs are often likened to Hermione Granger's bottomless handbag in the Harry Potter books: a tiny exterior concealing a seemingly infinite interior. Rice University chemist Stavroula Alina Kampouri has called MOFs "magical sponges", describing them as "not just elegant crystals you'd admire under a microscope; they're an entire universe of structures, each like a miniature city of tunnels and rooms waiting to be filled."'
Anjana Ahuja, Can molecular Lego save the planet?, Opinion Science. Financial Times, 15 October 2025, p.22.

individual
|
INTERPERSONAL : SCIENCES
humanistic -------------------------------------------  mechanistic
SOCIOLOGY : POLITICAL
|
group-population



'This is not an ivory-tower sort of topic, though: the importance of these sorts of complexes cannot be overstated. They were the basis for the first Nobel awarded in inorganic chemistry (1913, Alfred Werner) and metal coordination is how the iron atoms in hemoglobin carry oxygen to the cells of your body to keep you alive, for starters. You can say the same thing about photosynthesis in plants, and about the actions of the many crucial enzymes in every living creature on the planet that have metal-ion centers in them. Outside of biology and biochemistry, the structures of minerals similarly cannot be understood without a knowledge of coordination chemistry.'






The 2025 Nobel Prize in Chemistry: Metal-Organic Frameworks

Popular information. NobelPrize.org. Nobel Prize Outreach 2025. Mon. 27 Oct 2025. <https://www.nobelprize.org/prizes/chemistry/2025/popular-information/>

^Is this a question for BBC Radio 4 More or Less?

Of course, I keep posting about the Nobel Prize in the hope of a prize - due recognition for Hodges' model. Discretely of course, given a limited readership. 
Go figure: in 3D naturally.

Sunday, October 19, 2025

Space, Leadership, Choice, Politics II - Do Ho Soh

individual
|
INTERPERSONAL : SCIENCES
humanistic -------------------------------------------  mechanistic
SOCIOLOGY : POLITICAL
|
group-population


Who do we put on a pedestal?
                                                                               



Do Ho Suh's Public Figures features an empty pedestal held up by many small figures. Donny Bajohr



Do Ho Suh - Lehmann Maupin

Image: Smithsonian - Take a Closer Look at a Surprising New Sculpture That Rethinks Who We Put on a Pedestal

My source: Andy St. Louis, Sculptural approach to far-fetched ideas, Arts, Life&Arts, FTWeekend, 31 August/1 September 2024, p.12.



"There is another!" Karma (2003) by Do Ho Suh

Monday, October 06, 2025

On the 'front' - or behind the line(s)?

In many sources on socio-economics, politics, health policy ... I still note the challenge to represent the INDIVIDUAL and COLLECTIVE within a figure. Of course the author's subject, purpose, the context all influence the final depiction and the message to be conveyed. 

I wonder if Hodges' model can provide a starting point to explore relationships, oppositions, arguments and synergies?

Hodges' model provides an 
expansive and potentially powerful 'front' 
through its horizontal axis 
[ HUMANISTIC ↔ MECHANISTIC ].

This axis - drawn across and through the model vertically, may make it easier(?) to analyse and synthesize the relations at work and produce a diagram?

Individual
|
      INTERPERSONAL    :     SCIENCES               
HUMANISTIC =========================  MECHANISTIC      
 SOCIOLOGY  :    POLITICAL 
|
Group
INDIVIDUAL

INDIVIDUAL

GROUP - POPULATION

GROUP - POPULATION